共查询到19条相似文献,搜索用时 93 毫秒
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本文中我们证明了与实对角矩阵相似的每一个实循环矩阵都是对称的.并给出了一个正交变换,使得任意的n×n实循环对称矩阵通过该变换与实对角矩阵相似. 相似文献
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分析二次型与对称矩阵的对应关系,通过实例说明在实际教学中可能出现的问题.探讨正交变换的特点及其在二次型中的应用,并将此类应用推广到一般二次表达式. 相似文献
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作为《关于矩阵的特征值与特征向量同步求解问题》的续篇,利用其给出的方法,证明了新的定理.通过对实对称矩阵进行行列互逆变换,同步求出二次型的标准形及正交变换阵,简化了复杂的施密特正交化法,较好地解决了二次型标准形与正交变换阵同步求解问题. 相似文献
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用正交变换化实二次型为标准形方法研究 总被引:2,自引:0,他引:2
在线性代数的教学中,教师与学生常会遇到如下问题。(P) 设A为一n×n实对称矩阵,求一正交矩阵P使P~TAP为对角阵,其中P~T表示p的转置(这等价于经过正交变换X=PY,将二次 相似文献
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於崇华 《应用数学与计算数学学报》1989,3(1):43-47
§1.引言和记号 QL(或QR)算法是目前求解中小规模的对称矩阵的特征值问题的最有力工具。假定我们已通过正交变换把原矩阵约化成了三对角矩阵T,T是不可约的(即次对角元全不为零),记 相似文献
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一类特殊对称矩阵的特征值与特征向量 总被引:2,自引:0,他引:2
同济大学《线性代数》第130页例10要求一个正交变换.把二次型化为标准形,其中需要求矩阵的特征值与单位正交特征向量。事实上,这个矩阵R是一种具有特殊对称性的矩阵。这类矩阵的特征问题有如下的一般结论。考虑如下的特殊对称矩阵其中A、B均为m阶实对称阵,u是m维列向量,a是实数。求该类对称矩阵的特征值与特征向量的问题可转化为低阶对称矩阵的相应问题。定理1)设人,…,人是矩阵A-B的特征值,xl,…,X。是对应的单位正交特征向董;u;,…,u。是矩阵A+B的特征值,y;,…,y。是对应的单位正交特征向量,则人,…,入,户;… 相似文献
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<正> 任给二次型f=sum from i,i=1 to n (a_(ij)x_ix_j(a_(ij)=a(j1)),总有正交变换X=PY,使f化成标准形:f=λ_1y_1~2=…=λ_ny_n~2,其中λ_1,…,λ_n是f的矩阵A=(a_(ij))的特征值。这里我们只在实数范围内进行讨论。用正交变换化二次型为标准形的问题,也就是用正交矩阵P化实对称矩阵A为对角矩阵A的问题。这历来是教学中的重点和难点。一则由于这方面的内容有着广泛的应用,因而 相似文献
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本文研究了离散型随机变量次序统计量的分布矩阵的对称性 ,获得了二个定理 .定理 1 服从等概率二点分布或等概率三点分布的离散型随机变量的次序统计量的分布矩阵是对称矩阵 .定理 2 取值有限且等概率的离散型随机变量的次序统计量的分布矩阵具有中心对称性 . 相似文献
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The Riesz probability distribution on any symmetric cone and, in particular, on the cone of positive definite symmetric matrices represents an important generalization of the Wishart and of the matrix gamma distributions containing them as particular examples. The present paper is a continuation of the investigation of the properties of this probability distribution. We first establish a property of invariance of this probability distributions by a subgroup of the orthogonal group. We then show that the Pierce components of a Riesz random variable are independent, and we determine their probability distributions. Some moments and some useful expectations related to the Riesz probability distribution are also calculated. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
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一类矩阵方程的反中心对称最佳逼近解 总被引:3,自引:0,他引:3
利用矩阵的正交相似变换和广义奇异值分解,讨论了矩阵方程 AXB=C具有反中心对称解的充要条件,得到了解的具体表达式.然后应用Frobenius范数正交矩阵乘积不变性,在该方程的反中心对称解解集合中导出了与给定相同类型矩阵的最佳逼近解的表达式. 相似文献
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高维小波是处理多维信号的有力工具,张量积和栅格结构的小波有其自身的特点,但在实际应用中,我们仍需要构造小波滤波器来满足特定情形下的需要以提高滤波的效果,而构造正交滤波器,在多相域里就等价于构造仿酉阵,在本文中,我们通过对仿酉矩阵的研究,证明二元一次对称的仿酉阵一定能够块对角化,利用这种性质,给出了不可分离的二元正交小波滤波器组及线性相位小波滤波器的构造,并给出了相应的例子. 相似文献
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Raf Vandebril Ellen Van Camp Marc Van Barel Nicola Mastronardi 《Numerische Mathematik》2006,102(4):709-726
In this paper we describe an orthogonal similarity transformation for transforming arbitrary symmetric matrices into a diagonal-plus-semiseparable
matrix, where we can freely choose the diagonal. Very recently an algorithm was proposed for transforming arbitrary symmetric
matrices into similar semiseparable ones. This reduction is strongly connected to the reduction to tridiagonal form. The class
of semiseparable matrices can be considered as a subclass of the diagonalplus- semiseparable matrices. Therefore we can interpret
the proposed algorithm here as an extension of the reduction to semiseparable form.
A numerical experiment is performed comparing thereby the accuracy of this reduction algorithm with respect to the accuracy
of the traditional reduction to tridiagonal form, and the reduction to semiseparable form. The experiment indicates that all
three reduction algorithms are equally accurate. Moreover it is shown in the experiments that asymptotically all the three
approaches have the same complexity, i.e. that they have the same factor preceding the n3 term in the computational complexity. Finally we illustrate that special choices of the diagonal create a specific convergence
behavior.
The research was partially supported by the Research Council K.U.Leuven, project OT/05/40 (Large rank structured matrix computations),
by the Fund for Scientific Research–Flanders (Belgium), projects G.0078.01 (SMA: Structured Matrices and their Applications),
G.0176.02 (ANCILA: Asymptotic aNalysis of the Convergence behavior of Iterative methods in numerical Linear Algebra), G.0184.02
(CORFU: Constructive study of Orthogonal Functions) and G.0455.0 (RHPH: Riemann-Hilbert problems, random matrices and Padé-Hermite
approximation), and by the Belgian Programme on Interuniversity Poles of Attraction, initiated by the Belgian State, Prime
Minister's Office for Science, Technology and Culture, project IUAP V-22 (Dynamical Systems and Control: Computation, Identification
& Modelling). The scientific responsibility rests with the authors. 相似文献
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Sho Matsumoto 《Journal of Theoretical Probability》2012,25(3):798-822
We study a random positive definite symmetric matrix distributed according to a real Wishart distribution. We compute general moments of the random matrix and of its inverse explicitly. To do so, we employ the orthogonal Weingarten function, which was recently introduced in the study of Haar-distributed orthogonal matrices. As applications, we give formulas for moments of traces of a Wishart matrix and its inverse. 相似文献
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对A.Bunse-Gerstner和V.Mehrmann使用的一种随机辛阵的性质进行了研究.证明了1)其可以通过正交相似变换化为一种特殊的Schur标准型;2)其条件数为一常数;3)该常数约为2618. 相似文献